Categories > Units and Measurements > dimensions > A small steel ball of radius \[r\] is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity \[\eta \]. After some time the velocity of the ball attains a constant value known as terminal velocity \[{v_T}\]. The terminal velocity depends on (i) the mass of the ball \[m\], (ii) \[\eta \], (iii) \[r\] and (iv) acceleration due to gravity \[g\]. Which of the following relations is dimensionally correct

Units and Measurements

Question: A small steel ball of radius \[r\] is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity \[\eta \]. After some time the velocity of the ball attains a constant value known as terminal velocity \[{v_T}\]. The terminal velocity depends on (i) the mass of the ball \[m\], (ii) \[\eta \], (iii) \[r\] and (iv) acceleration due to gravity \[g\]. Which of the following relations is dimensionally correct


1) \[{v_T} \propto \frac{{mg}}{{\eta r}}\]
2) \[{v_T} \propto \frac{{\eta r}}{{mg}}\]
3) \[{v_T} \propto \eta rmg\]
4) \[{v_T} \propto \frac{{mgr}}{\eta }\]
Solution: Explanation: Explanation
dimensions

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